AG Lie-Gruppen: Jonas Schober, FAU

Vortragender: Jonas Schober, FAU
Veranstalter: Karl-Hermann Neeb

Titel: One-parameter semigroups of unitary endomorphisms of standard subspaces

Abstract:

Starting with a von Neumann algebra that has a cyclic and separating vector,
the
Tomita-Takesaki theory allows to translate this setting to the theory of
standard subspaces. Here, motivated by the Haag-Kastler theory of local
observables in Quantum Field Theory, one considers certain groups of unitary
operators and is interested in the semigroup of these unitaries that map the
standard subspace into itself. Classical results in this context are given in
the works of Borchers and Wiesbrock and by Longo/Witten.

In my PhD project I primarily focus on one-parameter semigroups of unitary
endomorphisms of standard subspaces. I show a way how to link these to
reflection positive Hilbert spaces and Hankel operators and in this context I
investigate the unitary one-parameter semigroups appearing in the works by
Longo
and Witten that come from so called Pick functions.